Number Representation
Challenges for Theory
- Indisputably conceptual
- Abstract
- Not cross-culturally universal
- Shared with animals
Nativist
- Believe there to be beyond sensory information
- Some parts are innate
- There’s a core knowledge of numbers
Empiricist
- Numbers are sensory representations by forming associations and detecting correlations
- Learned and constructed from sensory representations
Biological/fMRI
- Social and ecological reasons to know numbers
- For exact numbers: left inferior frontal lobe
- For approximate numbers: bilateral parietal lobe
- = different systems
The number sense (approximate)
- Evolutionary ancient
- Non-verbal system auto compute the approximate number of items in a set
- Available to animals, infants, and adults
- Continuous throughout lifespan
Adults Numerousity Discrimination
- Signature #1 (ratio): discriminability depends on the ratio
- Signature #2 (abstract): cross-modality (addition too)
- Signature #3 (arithmetric computations): addition and subtraction w/ approx number reps
- Without verbal counting
Infants Numerousity Discrimination
- Signature #1 (ratio): critical ratio = 2 (adult = 1.15), decline with age with experience
- Signature #2 (abstract): cross-modality in sounds
, - Signature #3 (arithmetic computations): addition and subtraction, look at strange
outcomes
- Can discriminate large magnitudes before learning to count, experiences like math ed and
non-specific experiences (visual acuity) increase ability
Animals Numerousity Discrimination
- Signature #1 (ratio): ratio limits shown in rats pressing for food
- Signature #2 (abstract): cross-modal in tamarin monkeys, rats in flash/tone
- Signature #3 (arithmetic computations): cayo santiago monkeys addition and subtraction
dropping lemon in box with surprise/attention test
- Adult monkeys can discriminate like a 9 month old, trained discrinimation close to adults
Culture Study
- Positive integers
- Piraha in Amazon: limited reading, no money, no external rep, monolingual
- No specific numbers (one/few, two/some, many)
- Using line tasks: not accurate beyond 3 items, not capable of representing exact large
numbers
- = representing numbers approximately but not exactly
Learning/Counting
- 24months/2yrs: can count but do not understand the meaning
- 30months: understand one
- 36months: understand two
- 40months: understand three
- 45moths: understand +1 is one more object = understand positive integers
Origins of Natural Number
- Primate heritage: represent objects, approximate numbers, singular/plural, serial order
- In human evolution: words, symbol system, conceptual change capabilities, analogy
Face Processing
Face Pareidolia: seeing faces in objects
For familiar face recognition, systems cope easily with different orientation
Bruce & Young Model for viewing faces
Challenges for Theory
- Indisputably conceptual
- Abstract
- Not cross-culturally universal
- Shared with animals
Nativist
- Believe there to be beyond sensory information
- Some parts are innate
- There’s a core knowledge of numbers
Empiricist
- Numbers are sensory representations by forming associations and detecting correlations
- Learned and constructed from sensory representations
Biological/fMRI
- Social and ecological reasons to know numbers
- For exact numbers: left inferior frontal lobe
- For approximate numbers: bilateral parietal lobe
- = different systems
The number sense (approximate)
- Evolutionary ancient
- Non-verbal system auto compute the approximate number of items in a set
- Available to animals, infants, and adults
- Continuous throughout lifespan
Adults Numerousity Discrimination
- Signature #1 (ratio): discriminability depends on the ratio
- Signature #2 (abstract): cross-modality (addition too)
- Signature #3 (arithmetric computations): addition and subtraction w/ approx number reps
- Without verbal counting
Infants Numerousity Discrimination
- Signature #1 (ratio): critical ratio = 2 (adult = 1.15), decline with age with experience
- Signature #2 (abstract): cross-modality in sounds
, - Signature #3 (arithmetic computations): addition and subtraction, look at strange
outcomes
- Can discriminate large magnitudes before learning to count, experiences like math ed and
non-specific experiences (visual acuity) increase ability
Animals Numerousity Discrimination
- Signature #1 (ratio): ratio limits shown in rats pressing for food
- Signature #2 (abstract): cross-modal in tamarin monkeys, rats in flash/tone
- Signature #3 (arithmetic computations): cayo santiago monkeys addition and subtraction
dropping lemon in box with surprise/attention test
- Adult monkeys can discriminate like a 9 month old, trained discrinimation close to adults
Culture Study
- Positive integers
- Piraha in Amazon: limited reading, no money, no external rep, monolingual
- No specific numbers (one/few, two/some, many)
- Using line tasks: not accurate beyond 3 items, not capable of representing exact large
numbers
- = representing numbers approximately but not exactly
Learning/Counting
- 24months/2yrs: can count but do not understand the meaning
- 30months: understand one
- 36months: understand two
- 40months: understand three
- 45moths: understand +1 is one more object = understand positive integers
Origins of Natural Number
- Primate heritage: represent objects, approximate numbers, singular/plural, serial order
- In human evolution: words, symbol system, conceptual change capabilities, analogy
Face Processing
Face Pareidolia: seeing faces in objects
For familiar face recognition, systems cope easily with different orientation
Bruce & Young Model for viewing faces
